Safe Feedback Motion Planning: A Contraction Theory and $\mathcal{L}_1$-Adaptive Control Based Approach
This addresses safety-critical applications for autonomous robots, offering a provably safe method that is incremental as it builds on existing motion planning algorithms.
The paper tackles the problem of ensuring autonomous robots operate safely despite model uncertainties and disturbances by proposing a planner-agnostic framework that certifies safe tubes around trajectories, guaranteeing the robot stays within them. It demonstrates this approach using contraction theory and L1-adaptive control for nonlinear systems with uncertainties.
Autonomous robots that are capable of operating safely in the presence of imperfect model knowledge or external disturbances are vital in safety-critical applications. In this paper, we present a planner-agnostic framework to design and certify safe tubes around desired trajectories that the robot is always guaranteed to remain inside of. By leveraging recent results in contraction analysis and $\mathcal{L}_1$-adaptive control we synthesize an architecture that induces safe tubes for nonlinear systems with state and time-varying uncertainties. We demonstrate with a few illustrative examples how contraction theory-based $\mathcal{L}_1$-adaptive control can be used in conjunction with traditional motion planning algorithms to obtain provably safe trajectories.